1 1 1 k Id ImK

Since only the volatile part of the analyte amount can traverse the membrane, it follows that:

where JL is the mass flux of the solvent through the separation membrane and P is the water permeability of the membrane. The osmotic pressure difference is multiplied by the reflection coefficient fR, which is a measure of the solute rejection by the membrane. During the enrichment process in the donor solution the osmotic pressure difference n increases. The driving force decreases. When the rejection is sufficiently high, the reflection coefficient fR approximates to unity. The rejection ratio is c

Figure 4 Reverse osmosis with concentration polarization on the asymmetric separation membrane. J, mass flux of the solute; pD, outer pressure from the donor solution; pA, outer pressure from the acceptor solution; nD and osmotic pressures of the donor and the acceptor solution respectively; <5c, thickness of the polarization layer; c d, solute concentration in the donor solution; c,dm, solute concentration on the membrane; c,m, solute concentration in the separation membrane. See text for further explanation.

defined by eqn [SC]:

The analytical usefulness is based on the high enrichment factor E, which can be achieved following by eqn [32]:

Ci,D

Figure 4 Reverse osmosis with concentration polarization on the asymmetric separation membrane. J, mass flux of the solute; pD, outer pressure from the donor solution; pA, outer pressure from the acceptor solution; nD and osmotic pressures of the donor and the acceptor solution respectively; <5c, thickness of the polarization layer; c d, solute concentration in the donor solution; c,dm, solute concentration on the membrane; c,m, solute concentration in the separation membrane. See text for further explanation.

where ci,A is the solute concentration in the filtrate, and ci;D;0 is the initial concentration in the donor solution. The rejected solutes accumulates on the membrane surface (Figure 4). This is the so-called concentration polarization phenomenon, which can be described approximately according to eqn [31]:

where cijDM is the solute concentration on the membrane surface and kL is the mass transfer coefficient.

The concentration up to the saturation level will cause the precipitation of the solute. The precipitated solute forms a secondary layer on the membrane, which reduces the solvent mass transfer JL. Therefore the concentration polarization must be reduced by a forced convective flow.

where VD 0 is the initial volume of the donor solution. Geometric Aspects

The geometric shape and extent both of the donor and the acceptor chambers is decisive for the effectiveness and time of the entire separation process. The geometry has to be adapted to the particular analytical task (Table 1). To minimize the separation time the thickness of the donor solution layer should be as thin as possible. The ratio of the membrane exchange area to the donor solution volume should be maximized. To maximize the enrichment factor for dialysis with enhanced selectivity the volume ratio between the donor solution and the acceptor solution has to be maximized.

In this respect, thin hollow-fibre membranes are especially useful both for enrichment and purification procedures. Thin-layer chambers with flat membranes are also useful and enable a greater variety of different membrane materials to be used. The miniaturization of the membrane exchange area up to the micro or the ultramicro scale enables reproducible sampling from quiescent or slowly flowing solutions to be performed. This is of great importance for in vivo sampling with microdialytic probes.

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